The solution of the spde in equation (REF ), which is a GF with Matèrn covariance function, can be approximated by a Matèrn Gaussian random field. The approximation uses a discretization process called the Finite Element Method which starts by defining a triangulation in \(\mathbb {R}^d\)  [1]}, [2]}. The observed locations are usually used as the initial vertices in the triangulation, and then additional vertices are added given some constraints such as maximum edge length and minimum interior angles. The next step is to define a basis function representation of \(x(\mathbf {s})\)  using the triangulation in \(\mathbb {R}^d\) , given by
\(x(\mathbf {s}) = \sum _{k=1}^{K}\psi _k(\mathbf {s})w_k\) 
